Automobile collision insurance is used to pay for any claims made against the driver in the event of an accident. This type of insurance will typically pay to repair any assets that your vehicle damages. A random sample of 40 collision claims of 20- to 24-year-old drivers results in a mean claim of $4540 with a standard deviation of $2315. An independent random sample of 40 collision claims of 30- to 59-year-old drivers results in a mean claim of $3660 with a standard deviation of $2036. Using the concept of hypothesis testing, determine if a higher insurance premium should be paid by 20- to 24-year-old drivers. Use a a = 0.05 level of significance, and let population 1 be 20- to 24-year old drivers and population 2 be 30- to 59-year old drivers. Complete parts (a) through (e) below. (a) Collision claims tend to be skewed right. Why do you think this is the case? O A. There are a few very large collision claims relative to the majority of claims. O B. There are many large collision claims relative to the majority of claims. O C. There are no very large collision claims. (b) What type of test should be used? O A. A hypothesis test regarding the difference of two means using a matched-pairs design O B. Ahypothesis test regarding the difference between two population proportions from independent samples O C. A hypothesis test regarding two population standard deviations O D. A hypothesis test regarding the difference of two means using Welch's approximate t (c) Determine the null and alternative hypotheses. Họ: (d) Use technology to calculate the P-value. (Round to three decimal places as needed.) (e) Draw a conclusion based on the hypothesis test. Choose the correct answers below.

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**Title: Hypothesis Testing in Automobile Collision Insurance**

**Introduction:**
Automobile collision insurance is designed to cover claims made against the driver in the event of an accident. This type of insurance usually covers the cost of vehicle damages. We examine whether higher insurance premiums should be applied to 20- to 24-year-old drivers compared to 30- to 59-year-old drivers using hypothesis testing.

**Scenario:**
- A random sample of 40 claims from drivers aged 20 to 24 resulted in a mean claim of $4540 with a standard deviation of $2315.
- A random sample of 40 claims from drivers aged 30 to 59 revealed a mean claim of $3360 with a standard deviation of $2036.
- Let population 1 be 20- to 24-year-old drivers, and population 2 be 30- to 59-year-old drivers.
- Use a significance level (α) of 0.05.

**Tasks:**

**(a) Analysis of Collision Claims:**
Collision claims tend to be skewed to the right. Consider the following reasons:
- A. There are a few very large collision claims relative to most claims.
- B. There are many large collision claims relative to the majority of claims.
- C. There are no very large collision claims.

**(b) Selection of Hypothesis Test:**
Select the appropriate type of test:
- A. A hypothesis test regarding the difference of two means using a matched-pairs design.
- B. A test for difference between two population proportions.
- C. A test for two population standard deviations.
- D. A hypothesis test regarding the difference of two means using Welch’s approximation.

**(c) Formulating Hypotheses:**
Determine the null and alternative hypotheses for comparing the mean claims.

**Hypotheses:**
- H₀: [Insert appropriate null hypothesis]
- H₁: [Insert appropriate alternative hypothesis]

**(d) P-Value Calculation:**
Use technology to calculate the P-value. The P-value should be rounded to three decimal places.

**(e) Conclusion Based on Hypothesis Test:**
Based on the P-value and the hypotheses, draw a conclusion about whether a higher insurance premium should be charged to younger drivers.

**Conclusion Options:**
Choose the correct answer below:
- A. [Conclusion based on hypothesis test outcome]

This example demonstrates the application of hypothesis testing in determining insurance pricing strategies based
Transcribed Image Text:**Title: Hypothesis Testing in Automobile Collision Insurance** **Introduction:** Automobile collision insurance is designed to cover claims made against the driver in the event of an accident. This type of insurance usually covers the cost of vehicle damages. We examine whether higher insurance premiums should be applied to 20- to 24-year-old drivers compared to 30- to 59-year-old drivers using hypothesis testing. **Scenario:** - A random sample of 40 claims from drivers aged 20 to 24 resulted in a mean claim of $4540 with a standard deviation of $2315. - A random sample of 40 claims from drivers aged 30 to 59 revealed a mean claim of $3360 with a standard deviation of $2036. - Let population 1 be 20- to 24-year-old drivers, and population 2 be 30- to 59-year-old drivers. - Use a significance level (α) of 0.05. **Tasks:** **(a) Analysis of Collision Claims:** Collision claims tend to be skewed to the right. Consider the following reasons: - A. There are a few very large collision claims relative to most claims. - B. There are many large collision claims relative to the majority of claims. - C. There are no very large collision claims. **(b) Selection of Hypothesis Test:** Select the appropriate type of test: - A. A hypothesis test regarding the difference of two means using a matched-pairs design. - B. A test for difference between two population proportions. - C. A test for two population standard deviations. - D. A hypothesis test regarding the difference of two means using Welch’s approximation. **(c) Formulating Hypotheses:** Determine the null and alternative hypotheses for comparing the mean claims. **Hypotheses:** - H₀: [Insert appropriate null hypothesis] - H₁: [Insert appropriate alternative hypothesis] **(d) P-Value Calculation:** Use technology to calculate the P-value. The P-value should be rounded to three decimal places. **(e) Conclusion Based on Hypothesis Test:** Based on the P-value and the hypotheses, draw a conclusion about whether a higher insurance premium should be charged to younger drivers. **Conclusion Options:** Choose the correct answer below: - A. [Conclusion based on hypothesis test outcome] This example demonstrates the application of hypothesis testing in determining insurance pricing strategies based
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